Basic Gear Formulas (pg 3)

2.08 This section covers recommended tooth proportions and dimensions of blanks for generated straight bevel gears of tooth ratios in general industrial use.

2.09 Bevel gears in this system have unequal addendums and unequal tooth thicknesses, except for pairs having equal numbers of teeth. This is different from the common practice for spur gearing. In bevel gear cutting, the tooth thickness is controlled by machine adjustments instead of by the tools, making it possible to obtain tooth thickness according to requirements for balance of strength in gear and pinion. Consideration has been given to both surface durability and beam strength in determining the tooth proportions.

2.10 An advantage in designing bevel gears according to this system is that tables are available giving tooth data and machine settings, thus minimizing calculations.* If other tooth designs are used, the data must be determined specially.

2.11 Angular Bevel Gears are bevel gears whose shafts are set at an angle other than 90 degrees.

2.12 Backlash - Table 2.4 gives the recommended backlash when the gear and pinion are finished and assembled ready to run. Quality numbers referred to in the table are defined by the AGMA Gear Classification Manual, AGMA 390.02.

Table 2.4 Recommended Backlash
Diametral Pitch	Backlash
	AGMA Quality Number
	4 thru 6	7 thru 13
20 to 50	0.000 - 0.002	0.000 - 0.002
50 to 80	0.000 - 0.001	0.000 - 0.001
80 and finer	0.000 - 0.0007	0.000 - 0.0007
*These Tables are available through Gleason Works, Rochester, New York.

2.13 Wormgearing is generally divided into two categories, fine-pitch worm gearing and coarse-pitch worm gearing. Fine-pitch worm gearing is segregated from coarse-pitch worm gearing for the following reasons:

2.14 Fine-Pitch Wormgears are used largely to transmit motion rather than power. Tooth strength, except at the coaser end of the fine-pitch range, is seldom an important factor. Durability and accuracy, as they affect the transmission of uniform angular motion, are of greater importance. Housing constructions and lubricating methods are generally radically different in fine-pitch wormgearing.

2.15 Profile Deviations and tooth bearings cannot be determined to the same degree of accuracy as those of coarse-pitch worms and wormgears, because of their small size.

2.16 Wormgear cutting equipment generally available for fine-pitch gears has definite restrictions which limit the diameter and lead range, degree of accuracy and kind of tooth bearing obtainable.

2.17 Special consideration must be given to top lands in fine-pitch hardened worms and in gear cutting tools.

2.18 In fine-pitch worms and wormgears, interchangeability and high production are important factors. Individual matching of the worm to the gear, as is frequently practiced with coarse-pitch precision worms, is impractical in the case of worms of fine pitch.

2.19 The methods of production and inspection of fine-pitch wormgears are generally different from those of coarse pitch.

2.20 Proportions of worms and wormgears are given in table 2.5. The pitch relations are expressed by the following formulas:

Term	Symbol	Formula (in.)
Lead	I	nP_x
Pitch Diameter	d	I / (Õ tan l)
Outside Diameter	d_o	d + 2a
Safe Minimum Length of Threaded Portion of Worm	F_w
*This formula allows a sufficient length for fine-pitch worms.

Pitch Diameter	D	Np / Õ
Outside Diameter	D_o	2C - d + 2a
Min. Face Width of Wormgear	F_{G min}

Addendum	a	0.3183 P_n
Whole Depth	h_I	0.7003 P_n+0.002
Working Depth	h_k	0.6366 P_n
Clearance	c	h_I ^_-h_k
Tooth Thickness	t	0.5 Pn
Approx. Normal Pressure angle	Ø_n	20 deg
Center Distance	C	.5 (d+D)

Where:
	p = Circular Pitch of a Wormgear
	P_x = Axial Pitch of Worm
	P_n = Normal Circular Pitch of Worm and Wormgear
	= Px cos l = p cos y
	l = Lead Angle of Worm
	y = Helix Angle of Wormgear
	n = Number of Threads in Worm
	N = Number of Teeth in Wormgear